What is expand (1+x)^8 ?

The solution to expand (1+x)^8 is 1+8x+28x^2+56x^3+70x^4+56x^5+28x^6+8x^7+x^8

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expand (1+x)^8

expand

(1 + x)^{8}

1 + 8 x + 28 x^{2} + 56 x^{3} + 70 x^{4} + 56 x^{5} + 28 x^{6} + 8 x^{7} + x^{8}

Solution steps

(1 + x)^{8}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = x

= i = 0 \sum 8 (i 8) \cdot 1^{(8 - i)} x^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} x^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} x^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} x^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} x^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} x^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} x^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} x^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} x^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} x^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} x^{0} : 1

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 1^{7} x^{1} : 8 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 1^{6} x^{2} : 28 x^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} x^{3} : 56 x^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} x^{4} : 70 x^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} x^{5} : 56 x^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} x^{6} : 28 x^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} x^{7} : 8 x^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} x^{8} : x^{8}

= 1 + 8 x + 28 x^{2} + 56 x^{3} + 70 x^{4} + 56 x^{5} + 28 x^{6} + 8 x^{7} + x^{8}

- (x - 1)^{3}

\frac{m + 3}{m - 3} + \frac{m + 2}{m - 2}

\frac{448 u ^{3} y ^{3}}{900 u ^{2} y ^{11}}

(\frac{1}{x})^{2} - 1

(x - 3) (x - 3) (x - 3)

What is expand (1+x)^8 ?
The solution to expand (1+x)^8 is 1+8x+28x^2+56x^3+70x^4+56x^5+28x^6+8x^7+x^8